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Friday, September 27, 2013

New Yorker: ... Redshirting is the practice of holding a child back for an extra year before the start of kindergarten, named for the red jersey worn in intra-team scrimmages by college athletes kept out of competition for a year. It is increasingly prevalent among parents of would-be kindergartners. In 1968, four per cent of kindergarten students were six years old; by 1995, the number of redshirted first- and second-graders had grown to nine per cent. In 2008, it had risen to seventeen per cent. The original logic of the yearlong delay is rooted in athletics: athletes who are bigger and stronger tend to perform better, so why not bench the younger, smaller ones for a year? The logic was popularized in “Freakonomics,” in which the authors, Stephen J. Dubner and Steven D. Levitt, pointed out that élite soccer players were much more likely to have birthdays in the earliest months of the year—that is, they would have been the oldest in any group of students that used a January 1st cutoff for enrollment.

On the surface, redshirting seems to make sense in the academic realm, too. The capabilities of a child’s brain increase at a rapid pace; the difference between five-year-olds and six-year-olds is far greater than between twenty-five-year-olds and twenty-six-year-olds. An extra year can allow a child to excel relative to the younger students in the class. “Especially for boys, there is thought to be a relative-age effect that persists across sports and over time,” said Friedman. “Early investment of time and skill developments appears to have a more lasting impact.” Older students and athletes are often found in leadership positions—and who can doubt the popularity of the star quarterback relative to the gym-class weakling?

It’s this competitive logic, rather than genuine concern about a child’s developmental readiness, that drives redshirting. Many parents decide to redshirt their children not because they seem particularly immature or young but because they hope that the extra year will give them a boost relative to their peers. In light of modern competitive demands, why wouldn’t you want your child to have that edge? The psychologist Betsy Sparrow calls it “gaming the system”—and the data on who chooses to redshirt bears out that classification: the people most likely to redshirt their children are those who can most afford to do so—that is, the white and the wealthy. Families in the highest socioeconomic quintile are thirty-six per cent more likely to redshirt their children than those in the lowest, and while close to six per cent of white children are redshirted, the figure falls to two per cent for Hispanic children, and less than one per cent for their black peers.

The data, however, belies this assumption. While earlier studies have argued that redshirted children do better both socially and academically—citing data on school evaluations, leadership positions, and test scores—more recent analyses suggest that the opposite may well be the case: the youngest kids, who barely make the age cutoff but are enrolled anyway, ultimately end up on top—not their older classmates. When a group of economists followed Norwegian children born between 1962 and 1988, until the youngest turned eighteen, in 2006, they found that, at age eighteen, children who started school a year later had I.Q. scores that were significantly lower than their younger counterparts. Their earnings also suffered: through age thirty, men who started school later earned less. A separate study, of the entire Swedish population born between 1935 and 1984, came to a similar conclusion: in the course of the life of a typical Swede, starting school later translated to reduced over-all earnings. In a 2008 study at Harvard University, researchers found that, within the U.S., increased rates of redshirting were leading to equally worrisome patterns. The delayed age of entry, the authors argued, resulted in academic stagnation: it decreased completion rates for both high-school and college students, increased the gender gap in graduation rates (men fell behind women), and intensified socioeconomic differences.

As it turns out, the benefits of being older and more mature may not be as important as the benefits of being younger than your classmates. In 2007, the economists Elizabeth Cascio and Diane Whitmore Schanzenbach decided to analyze the data of Tennessee’s Project STAR—an experiment originally designed to test the effects of classroom size on learning—with a different set of considerations: How would the relative class composition affect student performance? Their approach differed from most studies of redshirting in one crucial way: the students had been assigned totally randomly to their kindergarten classrooms, with no option for parents to lobby for, say, a different teacher, a different school, or a class in which the child would have some other perceived or actual relative advantage. This led to true experimental variation in relative age and maturity. That is, the same student could be relatively younger in one class, but relatively older in another, depending on his initial class assignment. The researchers discovered that relatively more mature students didn’t have an academic edge; instead, when they looked at their progress at the end of kindergarten, and, later, when they reached middle school, they were worse off in multiple respects. Not only did they score significantly lower on achievement tests—both in kindergarten and middle school—they were also more likely to have been kept back a year by the time they reached middle school, and were less likely to take college-entrance exams. The less mature students, on the other hand, experienced positive effects from being in a relatively more mature environment: in striving to catch up with their peers, they ended up surpassing them. ...

Few researchers would dispute that, in the immediate term, being relatively bigger, quicker, smarter, and stronger is a good thing. Repeatedly, the studies have found exactly that—older kindergarten students perform better on tests, receive better teacher evaluations, and do better socially. But then, something happens: after that early boost, their performance takes a nosedive. By the time they get to eighth grade, any disparity has largely evened out—and, by college, younger students repeatedly outperform older ones in any given year.

Monday, September 23, 2013

[ See this 2015 post for updated statistics, normalized to size of school population. ]

Commenter LY linked to this CollegeConfidential analysis in an earlier thread. I can't vouch for its accuracy but I find it quite interesting. Keep in mind this is a lagging indicator with relatively low statistics. Nevertheless a simple analysis of population-normalized (i.e., per individual) probability of great alumni accomplishment (e.g., as calculated below) would show very strong correlation with cognitive ability of student body over time. Must be a coincidence -- we all know those tests don't measure anything real ;-)

Many throw around Nobel Prize affiliations as proof of quality of education. So I decided to compile a list of colleges and universities according to where Nobel Prize winners completed their undergraduate education.

First, the ground rules:

1. I only included winners of the prize for Chemistry, Economics, Literature, Medicine and Physics. I did not include winners of the Peace prize.

2. I decided to add Fields Medalists since their is no Prize for Mathematics and the Fields medal is extremely prestigious.

Most of the results were expected, although I was surprised at how few prize winners had graduated from several elite universities (especially Brown, Duke, Johns Hopkins, Michigan, Northwestern, Princeton and Stanford).

The conclusion, I think most will agree after seeing the numbers, is that one cannot rely on the production of Nobel Prize winners as an indicator of quality of undergraduate education because only 7 universities have produced more than 5!

The summarized list of universities according to the number of Nobel Prize winners (undergraduate degree only):

The secret that both Caltech and Ecole Normale understand is simple: sample as hard as possible from the right tail of the g and conscientiousness distribution (that's about all you can reliably measure; maybe throw in some maverick wacky personality or "I looove science!" for good measure), hire the best professors you can, and cross your fingers... Note this methodology optimizes the school's contributions to humanity, but sadly not its endowment. See Defining Merit.

If I had time I'd make a slight adjustment by removing Literature and Economics from the prize list (sorry!), and perhaps add the Turing Prize or something similar.

Saturday, September 21, 2013

Jonathan Wai and Max Nisen rank US universities by student ability level as measured by SAT/ACT for BusinessInsider (methodology). Note I think using SAT/ACT disadvantages Caltech/MIT because the ceiling on the math component is lower than for the verbal, and many (almost all?) techers hit that ceiling. An alternative method using a higher ceiling test would yield improved rankings for STEM focused schools.

I always guessed that the Caltech undergraduate cognitive ability threshold was roughly few per thousand (perhaps even 1 in 1000) in the general population -- that's what the test scores imply. Although the kids are smart there is still a broad distribution on campus in the ability to learn core subjects like the required two years of math and physics (keep in mind -- these are Caltech-level courses!).

Based on my experience I would guess that the threshold ability to understand (for example) quantum mechanics is pretty high. A good chunk of the Caltech class doesn't grasp QM despite taking a year of it as sophomores -- and these are hard working, self-selected kids, in addition to being very smart. In our U Oregon study of psychometric thresholds, we found that kids in the top 1% of math ability (say, SAT-M > 750) had only a 50% chance of graduating in the physics major with more A's than B's -- i.e., in-major GPA > 3.5. Note, thanks to grade inflation the in-major average GPA in physics, as in other majors at Oregon and at other public universities (vs even higher averages at private schools), is something like 3.2, so 3.5 is not a high threshold (about +0.5 SD).

In other words, asking someone to explain Schrodinger's equation and the two slit experiment to you is probably a better verification of high end cognitive ability than any standardized test. (I wrote verification because understanding of QM is a sufficient but not necessary indicator of brainpower... some very smart people never study QM ... too bad for them!)

Here's what Vernon Smith (Nobel Prize in econ; started as a physics major at Caltech but bailed into EE and then econ ;-) had to say:

The first thing to which one has to adapt is the fact that no matter how high people might sample in the right tail of the distribution for "intelligence," ... that sample is still normally distributed in performing on the materials in the Caltech curriculum. The second thing you learn, if you were reared with my naive background, is the incredible arrogance that develops in conjunction with the acquisition of what you ultimately come to realize is a really very, very small bit of knowledge compared with our vast human ignorance. ... the difference between Harvard and Caltech: "At Harvard they believe they are the best in the world; at Caltech they know they are the best in the world."

Friday, September 20, 2013

Timothy Bates, a professor of psychology at the University of Edinburgh, and an occasional commenter on this blog, has a new paper out, which looks quite interesting. [See comments for references to additional literature and an overview from Tim!]

Studies of intelligence in children reveal significantly higher heritability among groups with high socioeconomic status (SES) than among groups with low SES. These interaction effects, however, have not been examined in adults, when between-families environmental effects are reduced. Using 1,702 adult twins (aged 24–84) for whom intelligence assessment data were available, we tested for interactions between childhood SES and genetic effects, between-families environmental effects, and unique environmental effects. Higher SES was associated with higher mean intelligence scores. Moreover, the magnitude of genetic influences on intelligence was proportional to SES. By contrast, environmental influences were constant. These results suggest that rather than setting lower and upper bounds on intelligence, genes multiply environmental inputs that support intellectual growth. This mechanism implies that increasing SES may raise average intelligence but also magnifies individual differences in intelligence.

... When psychologists first started studying twins, they found identical twins much more likely to have similar IQs than fraternal ones. They concluded that IQ was highly "heritable"—that is, due to genetic differences. But those were all high SES twins. Erik Turkheimer of the University of Virginia and his colleagues discovered that the picture was very different for poor, low-SES twins. For these children, there was very little difference between identical and fraternal twins: IQ was hardly heritable at all. Differences in the environment, like whether you lucked out with a good teacher, seemed to be much more important.

In the new study, the Bates team found this was even true when those children grew up. IQ was much less heritable for people who had grown up poor. This might seem paradoxical: After all, your DNA stays the same no matter how you are raised. The explanation is that IQ is influenced by education. Historically, absolute IQ scores have risen substantially as we've changed our environment so that more people go to school longer.

Richer children have similarly good educational opportunities, so genetic differences among them become more apparent. And since richer children have more educational choice, they (or their parents) can choose environments that accentuate and amplify their particular skills. A child who has genetic abilities that make her just slightly better at math may be more likely to take a math class, so she becomes even better at math.

But for poor children, haphazard differences in educational opportunity swamp genetic differences. Ending up in a terrible school or one a bit better can make a big difference. And poor children have fewer opportunities to tailor their education to their particular strengths. ...

Thursday, September 19, 2013

We've soft-launched a blogging channel for researchers at Michigan State. If you're a faculty member, researcher or graduate student who blogs (or would like to start!) you are welcome to contribute! We're hoping to grow the list of contributors into the hundreds, if possible. There are about 2000 tenure stream faculty and 10,000 graduate students at MSU...

Saturday, September 14, 2013

Summary for those wishing to follow science but who can't do math: consider many pairs of individuals and ask to what extent similarity in genotype is related to similarity in phenotype (g score, specific ability score, height, weight, etc.). From this analysis one can estimate the extent to which genes influence phenotype (heritability), and to what extent the same genes are influencing two different traits (e.g., height and weight, or reading ability and general cognitive ability g). The bivariate method is described here in more detail.

"These results indicate that genes related to diverse neurocognitive processes have general rather than specific effects."

Abstract: Very different neurocognitive processes appear to be involved in cognitive abilities such as verbal and non-verbal ability as compared to learning abilities taught in schools such as reading and mathematics. However, twin studies that compare similarity for monozygotic and dizygotic twins suggest that the same genes are largely responsible for genetic influence on these diverse aspects of cognitive function. It is now possible to test this evidence for strong pleiotropy using DNA alone from samples of unrelated individuals. Here we used this new method with 1.7 million DNA markers for a sample of 2,500 unrelated children at age 12 to investigate for the first time the extent of pleiotropy between general cognitive ability (aka intelligence) and learning abilities (reading, mathematics and language skills). We also compared these DNA results to results from twin analyses using the same sample and measures. The DNA-based method revealed strong genome-wide pleiotropy: Genetic correlations were greater than 0.70 between general cognitive ability and language, reading, and mathematics, results that were highly similar to twin study estimates of genetic correlations. These results indicate that genes related to diverse neurocognitive processes have general rather than specific effects.

[GCTA] ... The bivariate method extends the univariate model by relating the pairwise genetic similarity matrix to a phenotypic covariance matrix between traits 1 and 2 (Lee et al. 2012). The eight principal components described earlier were used as covariates in our bivariate GCTA analyses; as mentioned in the previous section, all phenotypes were age- and sex-regressed prior to analysis.

Twin modelling. The twin design and model-fitting is discussed elsewhere (Plomin et al. 2013a). We fit a bivariate Cholesky decomposition using OpenMx (Boker et al. 2011), which provided a direct comparison with the bivariate GCTA. The correlated factor solution is the least restricted model allowing variables to correlate with one another via genetic, shared environment, and non-shared environment.

... Table 1 shows GCTA-estimated genetic correlations (and standard errors, SE) between ‘g’ and learning abilities for more than 2,238 12-year-old UK twins (randomly selecting only one member of each twin pair to control for potential confounds, such as birth order) based on 1.7 million SNPs measured from the Affymetrix 6.0 GeneChip or imputed from HapMap 2,3 and WTCCC controls (Trzaskowski et al. 2013). Genetic correlations are significant and substantial for all three comparisons—between ‘g’ and language (0.81), mathematics (0.74), and reading (0.89). The GCTA-estimated genetic correlations between ‘g’ and learning abilities are similar in magnitude to the GCTA-estimated genetic correlation between height and weight (0.76). In addition, Table 1 includes bivariate results for ‘g’ versus height and ‘g’ versus weight as ‘negative controls’; their phenotypic correlations are both 0.07. As expected, these comparisons yielded negligible and nonsignificant genetic correlations (−0.03 and −0.06, respectively).

... A more novel question, and central to the present paper, is why, as we have shown here, bivariate genetic correlations estimated by GCTA are as great as twin study estimates. The likely reason is that attenuation of the estimated additive genetic variance due to imperfect linkage disequilibrium between causal variants and genotyped SNPs applies to both the additive genetic variance of the two traits and to their additive genetic covariance by the same proportion. Thus, the GCTA estimate of the genetic correlation is unbiased because it is derived from the ratio between genetic covariance and the genetic variances of the two traits.

Are generalist genes all in the mind (cognition) or are they in the brain as well? That is, genetic correlations between cognitive and learning abilities might be epiphenomenal in the sense that multiple genetically independent brain mechanisms could affect each ability, creating genetic correlations among abilities. However, the genetic principles of pleiotropy (each gene affects many traits) and polygenicity (many genes affect each trait) lead us to predict that generalist genes have their effects further upstream, creating genetic correlations among brain structures and functions, a prediction that supports a network view of brain structure and function.

Friday, September 13, 2013

From a recent Businessweek interview with a pessimistic Michael Lewis. Lewis was a bond trader at Salomon after graduating from Princeton in Art History.

Has Silicon Valley replaced Wall Street as the place for bright young people to make their millions?

My sense is that even though the financial crisis has lessened the appeal of the big Wall Street firm, it’s still appealing to kids in school, for the simple reason that unlike Silicon Valley, where you do have to know something to break in, the barriers to entry on Wall Street are quite low once you have the [Ivy League] credentials. If you’re a certain kind of kid who doesn’t actually know anything about anything, Wall Street is still a great place to go.

Thursday, September 12, 2013

Voyager 1 has left the solar system -- the first space probe from Earth to do so. Like other US deep space probes, it was made at Caltech's JPL, and carries with it the secret message: DEI or "Dabney Eats It" :-)

They say DEI was written on the moon by Caltech alumnus and astronaut Harrison Schmitt (the twelfth and last man to walk on the moon), but I don't know whether this is true.

Tuesday, September 10, 2013

I've long argued to my physics colleagues that adjunct professors, selected mainly on the basis of teaching ability, will do as well teaching introductory material as high powered researchers who (often) view their teaching assignment as a burdensome load (as in "teaching load"). It's also true that communication becomes more difficult as the brainpower gap between professor and student increases. (Some wags doubt whether two individuals who differ by, say, > 2 SD in intelligence can really understand each other ...)

Even if you find the results of the paper below unconvincing (perhaps the effect is too small), they nevertheless did not find that adjuncts are worse lecturers than tenure stream faculty. Yes, former and present colleagues, there is an arb to be had here: equal (or better!) quality teaching for students at lower cost, freeing up researchers in the department to produce more scientific knowledge.

The Atlantic: We all know the stereotype about tenured college professors: great researchers, lazy teachers. After all, you don't get tenure by dazzling 18-year-olds with PowerPoints. You do it by convincing other academics you're a genius in your field who's going to bring boatloads of grant money and prestige to campus. And nobody ever won a grant by grading papers.

A gross oversimplification? Of course. But there might also be a hint of truth in the caricature, at least judging by a new study from Northwestern University. The paper--co-authored by university president Morton Schapiro, professor David Figlio, and consultant Kevin Soter of The Greatest Good--finds that faculty who aren't on the tenure-track appear to do a better job than their tenured/tenure-track peers when it comes to teaching freshmen undergraduates.

Previous studies have suggested that colleges tend to hurt their graduation rates by hiring more part-time and non-tenure faculty. But Shapiro and his team wanted to measure the impact of tenure on "genuine student learning," a notoriously tricky task. So how'd they do it? Using the transcripts of Northwestern freshmen from 2001 through 2008, the research team focused on two factors: inspiration and preparation.

To start, the team asked if taking a class from a tenure or tenure-track professor in their first term later made students more likely to pursue additional courses in that field. So, to borrow their example, if an undergrad took economics 101 from an adjunct, and political science 101 from a tenured professor, were they any more likely to sign up for additional poli sci classes. That's the inspiration part. Second, the researchers wanted to know if students who took their first course in a field from a tenure or tenure-track professor got better grades when they pursued more advanced coursework. So, if our hypothetical student took more classes in both economics and poli sci, what did they fare better in? That's the preparation part.

Turns out, tenured and tenure-track professors underperformed on both the inspiration and preparation fronts. Controlling for certain student characteristics, freshmen were actually about 7 percent more likely to take a second course in a given field if their first class was taught by an adjunct or non-tenure professor. They also tended to get higher grades in those future courses. Taking an intro class with a non-tenure track instructor increased a student's mark in their second class by between .06* and .12 grade points, depending on controls. The freshmen who got the biggest boost tended to be less academically qualified students, judged by SAT scores and such, in the hardest subjects. [Italics mine.]

As the study notes, these patterns held "for all subjects, regardless of grading standards or the qualifications of the students the subjects attracted..." In other words, the non-tenure-track faculty bested their more established colleagues every from English to Engineering.

This study makes use of detailed student-level data from eight cohorts of first-year students at Northwestern University to investigate the relative effects of tenure track/tenured versus non-tenure line faculty on student learning. We focus on classes taken during a student’s first term at Northwestern, and employ a unique identification strategy in which we control for both student-level fixed effects and next-class-taken fixed effects to measure the degree to which non-tenure line faculty contribute more or less to lasting student learning than do other faculty. We find consistent evidence that students learn relatively more from non-tenure line professors in their introductory courses. These differences are present across a wide variety of subject areas, and are particularly pronounced for Northwestern’s average students and less-qualified students.

This kind of study isn't really using Big Data by scientific standards, but it's an example of "evidence-based" research on higher education that is now made possible by electronic storage of student records and cheap computation. See also Data Mining the University: College GPA Predictions from SAT Scores and Nonlinear Psychometric Thresholds for Physics and Mathematics. The hiding places for "faith-based" theories of education are slowly disappearing -- at least for the numerate. When I discussed the use of adjuncts in past department meetings, I was confidently told by colleagues (who had not looked at any relevant data) that REAL! research physicists did a much better job in the classroom than mere adjuncts. I am dubious of this because many excellent researchers are lousy teachers and either lack the self-awareness to realize it, or just refuse to admit it.

Sunday, September 08, 2013

I recommend this long NYTimes article about recent efforts at Harvard Business School to increase gender equity. If nothing else, it provides some insight into HBS and "elite business" culture. The contrast with East Asian business culture couldn't be more stark -- the emphasis at HBS is on getting your (possibly superficial or wrong) opinion out there as assertively as possible. Talking assertively is, by itself, considered a good thing regardless of content. This is a problem for many women, but it's also a problem for good decision making at firms ...

NYTimes: ... Some students, like Sheryl Sandberg, class of ’95, the Facebook executive and author of “Lean In,” sailed through. Yet many Wall Street-hardened women confided that Harvard was worse than any trading floor, with first-year students divided into sections that took all their classes together and often developed the overheated dynamics of reality shows. Some male students, many with finance backgrounds, commandeered classroom discussions and hazed female students and younger faculty members, and openly ruminated on whom they would “kill, sleep with or marry” (in cruder terms). Alcohol-soaked social events could be worse.

... By graduation, the school had become a markedly better place for female students, according to interviews with more than 70 professors, administrators and students, who cited more women participating in class, record numbers of women winning academic awards and a much-improved environment, down to the male students drifting through the cafeteria wearing T-shirts celebrating the 50th anniversary of the admission of women. Women at the school finally felt like, “ ‘Hey, people like me are an equal part of this institution,’ ” said Rosabeth Moss Kanter, a longtime professor.

And yet even the deans pointed out that the experiment had brought unintended consequences and brand new issues. The grade gap had vaporized so fast that no one could quite say how it had happened. The interventions had prompted some students to revolt, wearing “Unapologetic” T-shirts to lacerate Ms. Frei for what they called intrusive social engineering. Twenty-seven-year-olds felt like they were “back in kindergarten or first grade,” said Sri Batchu, one of the graduating men.

Students were demanding more women on the faculty, a request the deans were struggling to fulfill. And they did not know what to do about developments like female students dressing as Playboy bunnies for parties and taking up the same sexual rating games as men. “At each turn, questions come up that we’ve never thought about before,” Nitin Nohria, the new dean, said in an interview.

The administrators had no sense of whether their lessons would last once their charges left campus. As faculty members pointed out, the more exquisitely gender-sensitive the school environment became, the less resemblance it bore to the real business world. “Are we trying to change the world 900 students at a time, or are we preparing students for the world in which they are about to go?” a female professor asked.

... The men at the top of the heap worked in finance, drove luxury cars and advertised lavish weekend getaways on Instagram, many students observed in interviews. Some belonged to the so-called Section X, an on-again-off-again secret society of ultrawealthy, mostly male, mostly international students known for decadent parties and travel.

Women were more likely to be sized up on how they looked, Ms. Navab and others found. Many of them dressed as if Marc Jacobs were staging a photo shoot in a Technology and Operations Management class. Judging from comments from male friends about other women (“She’s kind of hot, but she’s so assertive”), Ms. Navab feared that seeming too ambitious could hurt what she half-jokingly called her “social cap,” referring to capitalization. ...

The goal of equalizing female representation at hedge and venture funds, and in aggressive areas of finance or entrepreneurship, will be challenging. A recent Crimson poll of the Harvard freshman class revealed:

Crimson: ... The gender gap was also apparent in career choice. Men were far more likely to hope to eventually work in finance and entrepreneurship than women, while women were much more likely to aspire to careers in nonprofits and public service, health, and media or publishing. [ Note: these are super high achieving HARVARD kids in the survey, not state-U types ... no one has more "privilege" than they do, so I think it's fair to conclude that they might be expressing their relatively unconstrained actual preferences here. ]

Few were truly brilliant intellectually. Few were academically distinguished (plenty of good ivy league degrees, but very few brilliant mathematical minds, etc.).

A good number will be at Davos in 20 years time.

Performance beyond a certain level in the vast majority of fields (and business is certainly one of them) is principally a function of having no cognitive and personal qualities which fall below a (high, but not insanely high) hygene threshold -- and then multiplied by determination, of course.

Conscientiousness, in fact, is the best single stable predictor of job success for complex jobs (well established in personality psychometrics).

Very high intelligence actually negatively correlates with career success (Kotter), probably because smart people enjoy solving problems, rather than making money selling things -- which outside of quant trading, show business and sport is really the only way of being really successful.

There are some extremely intelligent people in business (by which I mean high IQ, not just wise or experienced), but you tend to find them in the corners of the business landscape with the richest intellectual pastures: some areas of law, venture capital, some cutting edge technology fields.

Steve Ballmer - for instance - might deafen you, but he would not dazzle you.

PS I don't know much about Ballmer, but others claim that he is actually exceptionally intelligent, as are the other MSFT billionaires Gates, Allen, Simonyi. None of these individuals has an MBA ;-)

Wednesday, September 04, 2013

When I gave an informal whiteboard talk on this topic at IQIM I remarked that after almost 30 years (Hawking first proposed that black holes destroy quantum information in 1974), theorists are still baffled by the black hole information paradox.

Three recent blog posts on the information problem and firewalls:

Scott Aaronson (see lively discussion), John Preskill (I stole the picture from John), Lubos Motl (I think Lubos has the physics right in his post but I would probably more polite to our colleagues about it ;-)

Earlier post on this blog. My recent paper -- see eqns (3)-(5) for discussion of density matrix similar to Motl's. Like Lubos and Preskill (and everyone else?), I was never convinced by Hawking's concession paper on the unitarity question, but I do acknowledge some similarities between his arguments and mine.